Hexagons in a Row - Inside Mathematics

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Fifth Grade 5 th Grade Task 2 Hexagons in a Row Student Task Core Idea 3 Patterns, Functions, and Algebra Find a pattern in a sequence of diagrams and use the pattern to make predictions. Find the total number of iterations of hexagons that can be made when the total number of toothpicks is given. Understand patterns and use mathematical models such as algebraic symbols and graphs to represent and understand quantitative relationships. • Represent and analyze patterns and functions using words, tables, and graphs • Investigate how a change in one variable relates to a change in a second variable. • Find the results of a rule for a specific value • Use inverse operations to solve multi-step problems • Use concrete, pictorial, and verbal representations to solve problems involving unknowns Mathematics in the task: • Extend a geometric pattern • Useatable • Work backwards • Understand the idea of a constant • Recognize when a pattern is not proportional Based on teacher observations, this is what fifth graders knew and were able to do: • Addontoanexistingpattern • Recognize and verbalize a pattern (going up by 5’s) • Add on, multiply or divide by 5 Areas of difficulty for fifth graders: • Multiplying by 6 instead of 5 (not noticing the overlap when hexagons are connected) • Not seeing that the first hexagon has needs more toothpicks than the rest • Seeing generalizable rules • Drawing and counting accurately • Dealing with the shared sides Strategies used by successful students: • Draw pictures • Extended the table • Seeing how the structural pattern of the hexagons grew and using that to form a rule Fifth Grade – 2006 Pg. (c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation: info@noycefdn.org. 37
MARS Test Task 2 Frequency Distribution and Bar Graph, Grade 5 Task 2 – Hexagons in a Row Mean: 5.14 StdDev: 2.71 Figure 35: Bar Graph of MARS Test Task 2 Raw Scores, Grade 5 MARS Task 2 Raw Scores The maximum score for this task is 8 points. The minimum score for a level 3 response, meeting standards, is 4 points. Most students, 93%, could extend the pattern by filling in the table. Many students, 81%, could extend the pattern beyond the table to 5 hexagons and explain that the pattern is growing by 5 each time. More than half the students, 68%, could also do some of the thinking to solve for 12 hexagons, but they may have made a counting or calculation error. About half the students could also find the number of hexagons that could be made with 76 toothpicks. 33% could meet all the demands of the task including finding the number of toothpicks needed to make 12 hexagons in a row. 7% of the students scored no points on this task. All the students in the sample with this score attempted the task. Fifth Grade – 2006 Pg. (c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation: info@noycefdn.org. 38
Page 1 and 2: Performance Assessment Task Hexagon
Page 3 and 4: Hexagons in a Row This problem give
Page 5 and 6: Hexagons in a Row Rubric The core e
Page 7 and 8: Looking at student work on Hexagons
Page 9 and 10: Student B2 also thinks about the 6+
Page 11 and 12: Student D is able to come up with t
Page 13 and 14: Student F is able to complete a tab
Page 15: Incorrect strategies included 5% tr
Page 19 and 20: Ideas for Action Research-Using Stu
Page 21 and 22: First Student Fifth Grade - 2006 Pg
Page 23 and 24: Student 3 Fifth Grade - 2006 Pg. (c
Page 25 and 26: For the next part the teacher wants

Hexagons in a Row - Inside Mathematics

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